= Elliptic function-field decomposition
{title2=$\mathbb C(\mathbb C/\Lambda)=\mathbb C(\wp)\oplus\wp^{\prime}\mathbb C(\wp)$}
Every <elliptic function> has a unique expression $A(\wp)+B(\wp)\wp^{\prime}$ with <rational functions> $A,B$. Its even part is rational in the <Weierstrass elliptic function>; its odd part divided by $\wp^{\prime}$ is even and meromorphic, so is also rational in $\wp$. The local even Laurent series at a half-period and at the pole justify meromorphic descent through the double cover of the <Riemann sphere>.
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